To solve this problem we will apply the given concept for torque which explains the relationship between the force applied and the distance to a given point. Mathematically this relationship is given as
Where,
Torque
F = Force
d = Distance
Our values are given as,
Therefore replacing we have that the force is
F = 12.72N
Therefore the least amount of force that you must exert is 12.72N
To solve the problem we will first start considering the Pressure given the hydrostatic definition of the product between the density, the gravity and the depth. We will define the area where the liquid acts and later we will use the definition of the force as a product between the pressure and the area to calculate the force given in the two depths. The gauge pressure at the depth x will be
This pressure acts on the strip of area
The force acting on that strip is given by,
To evaluate the force, we will then consider the integral of the pressure as a function of the Area, or the integral of the previously found terms.
Evaluating at the initial depth of 1.8m and the final depth of 4.4 we have then that,
Therefore the Net force will be